spectral_hex_map.hpp

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#ifndef MOAB_SPECTRAL_HEX_HPP
#define MOAB_SPECTRAL_HEX_HPP

#include "moab/Matrix3.hpp"
#include "moab/CartVect.hpp"
#include "moab/FindPtFuncs.h"
#include <sstream>
#include <iomanip>
#include <iostream>

namespace moab
{

namespace element_utility
{

    namespace
    {
    }  // namespace

    template < typename _Matrix >
    class Spectral_hex_map
    {
      public:
        typedef _Matrix Matrix;

      private:
        typedef Spectral_hex_map< Matrix > Self;

      public:
        // Constructor
        Spectral_hex_map(){};
        Spectral_hex_map( int order )
        {
            initialize_spectral_hex( order );
        }
        // Copy constructor
        Spectral_hex_map( const Self& f ) {}

      private:
        void initialize_spectral_hex( int order )
        {
            if( _init && _n == order )
            {
                return;
            }
            if( _init && _n != order )
            {
                free_data();
            }
            _init = true;
            _n    = order;
            for( int d = 0; d < 3; d++ )
            {
                lobatto_nodes( _z[d], _n );
                lagrange_setup( &_ld[d], _z[d], _n );
            }
            opt_alloc_3( &_data, _ld );
            std::size_t nf = _n * _n, ne = _n, nw = 2 * _n * _n + 3 * _n;
            _odwork = tmalloc( real, 6 * nf + 9 * ne + nw );
        }

        void free_data()
        {
            for( int d = 0; d < 3; d++ )
            {
                free( _z[d] );
                lagrange_free( &_ld[d] );
            }
            opt_free_3( &_data );
            free( _odwork );
        }

      public:
        // Natural coordinates
        template < typename Moab, typename Entity_handle, typename Points, typename Point >
        std::pair< bool, Point > operator()( const Moab& /* moab */,
                                             const Entity_handle& /* h */,
                                             const Points& v,
                                             const Point& p,
                                             const double tol = 1.e-6 )
        {
            Point result( 3, 0.0 );
            /*
            moab.tag_get_by_ptr(_xm1Tag, &eh, 1,(const void **) &_xyz[ 0] );
            moab.tag_get_by_ptr(_ym1Tag, &eh, 1,(const void **) &_xyz[ 1] );
            moab.tag_get_by_ptr(_zm1Tag, &eh, 1,(const void **) &_xyz[ 2] );
            */
            bool point_found = solve_inverse( p, result, v, tol ) && is_contained( result, tol );
            return std::make_pair( point_found, result );
        }

      private:
        void set_gl_points( double* x, double* y, double* z )
        {
            _xyz[0] = x;
            _xyz[1] = y;
            _xyz[2] = z;
        }
        template < typename Point >
        bool is_contained( const Point& p, const double tol ) const
        {
            // just look at the box+tol here
            return ( p[0] >= -1. - tol ) && ( p[0] <= 1. + tol ) && ( p[1] >= -1. - tol ) && ( p[1] <= 1. + tol ) &&
                   ( p[2] >= -1. - tol ) && ( p[2] <= 1. + tol );
        }

        template < typename Point, typename Points >
        bool solve_inverse( const Point& x, Point& xi, const Points& points, const double tol = 1.e-6 )
        {
            const double error_tol_sqr = tol * tol;
            Point delta( 3, 0.0 );
            xi = delta;
            evaluate( xi, points, delta );
            vec_subtract( delta, x );
            std::size_t num_iterations = 0;
#ifdef SPECTRAL_HEX_DEBUG
            std::stringstream ss;
            ss << "Point: ";
            ss << x[0] << ", " << x[1] << ", " << x[2] << std::endl;
            ss << "Hex: ";
            for( int i = 0; i < 8; ++i )
            {
                ss << points[i][0] << ", " << points[i][1] << ", " << points[i][2] << std::endl;
            }
            ss << std::endl;
#endif
            while( normsq( delta ) > error_tol_sqr )
            {
#ifdef SPECTRAL_HEX_DEBUG
                ss << "Iter #: " << num_iterations << " Err: " << sqrt( normsq( delta ) ) << " Iterate: ";
                ss << xi[0] << ", " << xi[1] << ", " << xi[2] << std::endl;
#endif
                if( ++num_iterations >= 5 )
                {
                    return false;
                }
                Matrix J;
                jacobian( xi, points, J );
                double det = moab::Matrix::determinant3( J );
                if( fabs( det ) < 1.e-10 )
                {
#ifdef SPECTRAL_HEX_DEBUG
                    std::cerr << ss.str();
#endif
#ifndef SPECTRAL_HEX_DEBUG
                    std::cerr << x[0] << ", " << x[1] << ", " << x[2] << std::endl;
#endif
                    std::cerr << "inverse solve failure: det: " << det << std::endl;
                    exit( -1 );
                }
                vec_subtract( xi, moab::Matrix::inverse( J, 1.0 / det ) * delta );
                evaluate( xi, points, delta );
                vec_subtract( delta, x );
            }
            return true;
        }

        template < typename Point, typename Points >
        Point& evaluate( const Point& p, const Points& /* points */, Point& f )
        {
            for( int d = 0; d < 3; ++d )
            {
                lagrange_0( &_ld[d], p[0] );
            }
            for( int d = 0; d < 3; ++d )
            {
                f[d] = tensor_i3( _ld[0].J, _ld[0].n, _ld[1].J, _ld[1].n, _ld[2].J, _ld[2].n, _xyz[d], _odwork );
            }
            return f;
        }

        template < typename Point, typename Field >
        double evaluate_scalar_field( const Point& p, const Field& field ) const
        {
            int d;
            for( d = 0; d < 3; d++ )
            {
                lagrange_0( &_ld[d], p[d] );
            }
            return tensor_i3( _ld[0].J, _ld[0].n, _ld[1].J, _ld[1].n, _ld[2].J, _ld[2].n, field, _odwork );
        }
        template < typename Points, typename Field >
        double integrate_scalar_field( const Points& p, const Field& field ) const
        {
            // set the position of GL points
            // set the positions of GL nodes, before evaluations
            _data.elx[0] = _xyz[0];
            _data.elx[1] = _xyz[1];
            _data.elx[2] = _xyz[2];
            double xi[3];
            // triple loop; the most inner loop is in r direction, then s, then t
            double integral = 0.;
            // double volume = 0;
            int index = 0;  // used fr the inner loop
            for( int k = 0; k < _n; k++ )
            {
                xi[2] = _ld[2].z[k];
                // double wk= _ld[2].w[k];
                for( int j = 0; j < _n; j++ )
                {
                    xi[1] = _ld[1].z[j];
                    // double wj= _ld[1].w[j];
                    for( int i = 0; i < _n; i++ )
                    {
                        xi[0] = _ld[0].z[i];
                        // double wi= _ld[0].w[i];
                        opt_vol_set_intp_3( (opt_data_3*)&_data, xi );  // cast away const-ness
                        double wk = _ld[2].J[k];
                        double wj = _ld[1].J[j];
                        double wi = _ld[0].J[i];
                        Matrix3 J( 0. );
                        for( int n = 0; n < 8; n++ )
                            J( n / 3, n % 3 ) = _data.jac[n];
                        double bm = wk * wj * wi * J.determinant();
                        integral += bm * field[index++];
                        // volume +=bm;
                    }
                }
            }
            // std::cout << "volume: " << volume << "\n";
            return integral;
        }

        template < typename Point, typename Points >
        Matrix& jacobian( const Point& /* p */, const Points& /* points */, Matrix& J )
        {
            real x[3];
            for( int i = 0; i < 3; ++i )
            {
                _data.elx[i] = _xyz[i];
            }
            opt_vol_set_intp_3( &_data, x );
            for( int i = 0; i < 9; ++i )
            {
                J( i % 3, i / 3 ) = _data.jac[i];
            }
            return J;
        }

      private:
        bool _init;
        int _n;
        real* _z[3];
        lagrange_data _ld[3];
        opt_data_3 _data;
        real* _odwork;
        real* _xyz[3];
    };  // Class Spectral_hex_map

}  // namespace element_utility

}  // namespace moab
#endif  // MOAB_SPECTRAL_HEX_nPP